InterviewSolution
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Show that the function f defined by f(x)={(x if "x is rational"),(-x if "x is irrational"):} is continuous at x=0 AAxne0inR |
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Answer» Solution :f(0)=0 L.H.L=`lim_(xto0)f(x)=lim_(hto0)f(-h)` `=lim_(hto0){(-h if "h is RATIONAL" =0),(h if "h is irrational"):}` Similarly R.H.L.=0 THUS L.H.L.=R.H.L.=f(0) Hence f(x) is continuous at x=0 We can easily show that f(x) is discontinuous at all real POINTS `xne0` |
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